{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Theano\n",
" \n",
" (1) Theano\n",
" \n",
" Theano is a Python library that allows you to define, optimize, and evaluate mathematical expressions involving multi-dimensional arrays efficiently. \n",
" \n",
" Theano features:\n",
" \n",
" - tight integration with NumPy – Use numpy.ndarray in Theano-compiled functions.\n",
" - transparent use of a GPU – Perform data-intensive calculations up to 140x faster than with CPU.(float32 only)\n",
" - efficient symbolic differentiation – Theano does your derivatives for function with one or many inputs.\n",
" - speed and stability optimizations – Get the right answer for log(1+x) even when x is really tiny.\n",
" - dynamic C code generation – Evaluate expressions faster.\n",
" - extensive unit-testing and self-verification – Detect and diagnose many types of mistake.\n",
" \n",
" Theano has been powering large-scale computationally intensive scientific investigations since 2007. But it is also approachable enough to be used in the classroom\n",
" \n",
" (2) Install\n",
" \n",
" Basic user install instructions\n",
" \n",
" pip install Theano OR pip install Theano --user\n",
" \n",
" update\n",
" \n",
" sudo pip install --upgrade --no-deps theano\n",
" \n",
" The following command will update Theano and Numpy/Scipy (warning bellow):\n",
" \n",
" sudo pip install --upgrade theano\n",
"\n",
"2. Numpy\n",
"\n",
" [1] Matrix conventions\n",
" \n",
" (1) Array Creation\n",
" \n",
" array()"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 6. , 7.5, 8. , 0. , 1. ])"
]
},
"execution_count": 1,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"import numpy as np\n",
"\n",
"data1 = [6, 7.5, 8, 0, 1]\n",
"\n",
"arr1 = np.array(data1)\n",
"\n",
"arr1"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" arrange()"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.arange(10)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 2., 3., 4., 5., 6., 7., 8., 9.])"
]
},
"execution_count": 3,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.arange(2, 10, dtype=np.float)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 2. , 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9])"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.arange(2, 3, 0.1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" indices()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[[0, 0, 0],\n",
" [1, 1, 1],\n",
" [2, 2, 2]],\n",
"\n",
" [[0, 1, 2],\n",
" [0, 1, 2],\n",
" [0, 1, 2]]])"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"np.indices((3,3))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" (2) Indexing\n",
" \n",
" single element indexing"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"2"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.arange(10)\n",
"\n",
"x[2]\n"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x[-2]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"8"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x.shape = (2,5)\n",
"x[1,3]"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"9"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x[1,-1]"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2, 3, 4])"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x[0]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Other indexing options"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([2, 3, 4])"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.arange(10)\n",
"x[2:5]"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([0, 1, 2])"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x[:-7]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([1, 3, 5])"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x[1:7:2]"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 7, 10, 13],\n",
" [21, 24, 27]])"
]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y = np.arange(35).reshape(5,7)\n",
"y[1:5:2,::3]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" (3) Index Arrays"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([7, 7, 9, 2])"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x = np.arange(10,1,-1)\n",
"x[np.array([3, 3, 1, 8])]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" It is an error to have index values out of bounds:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "IndexError",
"evalue": "index 20 is out of bounds for size 9",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mIndexError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-17-3ad16747a54d>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m8\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mIndexError\u001b[0m: index 20 is out of bounds for size 9"
]
}
],
"source": [
" x[np.array([3, 3, 20, 8])]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" (4) Indexing Multi-dimensional arrays"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 0, 15, 30])"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y[np.array([0,2,4]), np.array([0,1,2])]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" If the index arrays do not have the same shape, there is an attempt to \n",
" broadcast them to the same shape. If they cannot be broadcast to \n",
" the same shape, an exception is raised:"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "ValueError",
"evalue": "shape mismatch: objects cannot be broadcast to a single shape",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-19-1a836a248e48>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0my\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mValueError\u001b[0m: shape mismatch: objects cannot be broadcast to a single shape"
]
}
],
"source": [
"y[np.array([0,2,4]), np.array([0,1])]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 1, 15, 29])"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"y[np.array([0,2,4]), 1]"
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 0, 1, 2, 3, 4, 5, 6],\n",
" [14, 15, 16, 17, 18, 19, 20],\n",
" [28, 29, 30, 31, 32, 33, 34]])"
]
},
"execution_count": 21,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
" y[np.array([0,2,4])]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" [2] BroadCasting\n",
" The term broadcasting describes how numpy treats arrays with different shapes during arithmetic operations. Subject to certain constraints, the smaller array is \n",
" “broadcast” across the larger array so that they have compatible shapes\n",
" \n",
" @Rules\n",
" \n",
" When operating on two arrays, NumPy compares their shapes element-wise. \n",
" It starts with the trailing dimensions, and works its way forward. \n",
" Two dimensions are compatible when\n",
" \n",
" they are equal, or\n",
" one of them is 1\n",
" \n",
" If these conditions are not met, a ValueError: frames are not aligned exception\n",
" is thrown, indicating that the arrays have incompatible shapes. \n",
" The size of the resulting array is the maximum size along each dimension of the \n",
" input arrays.\n",
" "
]
},
{
"cell_type": "code",
"execution_count": 22,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([ 2., 4., 6.])"
]
},
"execution_count": 22,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"a = np.array([1.0, 2.0, 3.0])\n",
"b = np.array([2.0, 2.0, 2.0])\n",
"a * b"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" Two Dimensions are not compatible ( x is (4,) , y is (5,) )"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {
"collapsed": false
},
"outputs": [
{
"ename": "ValueError",
"evalue": "operands could not be broadcast together with shapes (4,) (5,) ",
"output_type": "error",
"traceback": [
"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mValueError\u001b[0m Traceback (most recent call last)",
"\u001b[0;32m<ipython-input-24-f7f60ee3cd0e>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mz\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mones\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 6\u001b[0;31m \u001b[0mx\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
"\u001b[0;31mValueError\u001b[0m: operands could not be broadcast together with shapes (4,) (5,) "
]
}
],
"source": [
"x = np.arange(4)\n",
"xx = x.reshape(4,1)\n",
"y = np.ones(5)\n",
"z = np.ones((3,4))\n",
"\n",
"x + y"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 1., 1., 1., 1.],\n",
" [ 2., 2., 2., 2., 2.],\n",
" [ 3., 3., 3., 3., 3.],\n",
" [ 4., 4., 4., 4., 4.]])"
]
},
"execution_count": 25,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"xx + y"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"array([[ 1., 2., 3., 4.],\n",
" [ 1., 2., 3., 4.],\n",
" [ 1., 2., 3., 4.]])"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"x + z"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"(3, 4)"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(x + z).shape"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.6"
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"nbformat_minor": 0
}